st: one way anova or kruskal wallis if sample size is less than 3 for each group

[<redacted>]

Dear all, 

this is my first ever posting to statalist. 

I have a data with 5 groups (group) and a quantitative dependent variable (score). Two groups have sample size of two and 4 groups have sample size of 3. 

I run kruskal wallis test and because the P-value is less than 0.05, i do Mann-whitney test. I am baffled that none of the p value from Mann whitney test is less than 0.05. I also run one-way anova with bonferroni correction, and the results show p values of less than 0.05. 

Can someone explain this and which test should i choose? 

Thank you very much 


KRUSKAL WALLIS 

. kwallis score, by(group) 

Kruskal-Wallis equality-of-populations rank test 

+------------------------+ 
| group | Obs | Rank Sum | 
|-------+-----+----------| 
| 1 | 2 | 29.00 | 
| 2 | 2 | 3.00 | 
| 3 | 3 | 12.00 | 
| 4 | 3 | 21.00 | 
| 5 | 3 | 41.00 | 
|-------+-----+----------| 
| 6 | 3 | 30.00 | 
+------------------------+ 

chi-squared = 14.309 with 5 d.f. 
probability = 0.0138 

chi-squared with ties = 14.330 with 5 d.f. 
probability = 0.0136 

. ranksum score if group == 1 | group ==2, by(group) 

Two-sample Wilcoxon rank-sum (Mann-Whitney) test 

group | obs rank sum expected 
-------------+--------------------------------- 
1 | 2 7 5 
2 | 2 3 5 
-------------+--------------------------------- 
combined | 4 10 10 

unadjusted variance 1.67 
adjustment for ties 0.00 
---------- 
adjusted variance 1.67 

Ho: score(group==1) = score(group==2) 
z = 1.549 
Prob > |z| = 0.1213 

*** other Mann-Whitney results not shown 


ONE WAY ANOVA 

. oneway score group, bonferroni 

Analysis of Variance 
Source SS df MS F Prob > F 
------------------------------------------------------------------------ 
Between groups 43047.0833 5 8609.41667 106.20 0.0000 
Within groups 810.666667 10 81.0666667 
------------------------------------------------------------------------ 
Total 43857.75 15 2923.85 

Bartlett's test for equal variances: chi2(5) = 9.2622 Prob>chi2 = 0.099 

Comparison of score by group 
(Bonferroni) 
Row Mean-| 
Col Mean | 1 2 3 4 5 
---------+------------------------------------------------------- 
2 | -133 
| 0.000 
| 
3 | -125 8 
| 0.000 1.000 
| 
4 | -111.667 21.3333 13.3333 
| 0.000 0.400 1.000 
| 
5 | -8 125 117 103.667 
| 1.000 0.000 0.000 0.000 
| 
6 | -70 63 55 41.6667 -62 
| 0.000 0.000 0.000 0.003 0.000 




Best regards 




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